This invention relates to NMR imaging and more particularly relates to NMR imaging of samples of materials to determine transport properties of such samples.
The oil industry makes extensive use of various transport properties of earth formations to determine the amount of hydrocarbon reserves and the producibility of these reserves. Among these transport properties of earth formations are diffusion coefficients, electrical resistivity factors and permeability to fluid flow. These properties relate to Fick's law concentration transport, electric current transport, and hydraulic fluid transport, respectively, through porous and permeable earth formations, or representative samples thereof.
The oil industry makes extensive use of electrical resistivity well logging for open hole evaluation of the oil saturation in earth formations. In the interpretation of electrical resistivity well logs, the major unknown quantity is often the formation resistivity factor, F. The formation resistivity factor measures the influence of pore structure on the resistance of the sample. F is defined via Archie's relation: EQU C.sub.o =S.sub.w.sup.n (1/F)C.sub.w ( 1)
where:
C.sub.o is the conductivity of the formation, S.sub.w is the brine saturation, n is the saturation exponent, F is the formation resistivity factor, and C.sub.w is the brine conductivity.
When the oil saturation is zero, this equation reduces to: EQU C.sub.o =(1/F)C.sub.w ( 2)
The electrical resistivity well log measures the formation conductivity, C.sub.o. The brine conductivity C.sub.w is often known from produced brine or can be estimated from other logs such as the spontaneous potential log. The saturation exponent n is approximately equal to 2. Thus, a major unknown quantity needed for accurate well log evaluation is the formation resistivity factor, F. Once F is known, the brine saturation, S.sub.w, and the hydrocarbon saturation, S.sub.o =1-S.sub.w, can then be determined from the electrical resistivity well logs. The basic equations above are often modified to reflect the presence of clay minerals inside the pore space of the earth formation, as is well known in the art. For example, the Waxman-Smits equation for water-saturated shaly sands is EQU C.sub.o =(1/F)(C.sub.w +BQ.sub.v),
where B is the equivalent conductivity of the clay exchange counterions and Q.sub.v the cation exchange capacity of the clay minerals. Similarly, for oil bearing shaly sands the Waxman-Smits equation is: EQU C.sub.o =S.sub.w.sup.n /F[C.sub.w +(BQ.sub.v /S.sub.w)].
In order to determine the formation resistivity factor, earth material is cored from the well of interest and then analyzed in a laboratory. The laboratory procedure for measuring formation resistivity factor is to first drill small core plugs from the core sample. The core plugs are then cleaned of all oil and brine in extraction vessels, such as Dean-Stark extractors, which are well known in the art. The core plugs are then saturated with a plurality of brines of known conductivities, and the resistivity of the core plugs are measured while saturated with each brine.
For core samples that contain clay minerals, long periods of time are required for the core sample to equilibrate with the injected brines. Since this is a slow and laborious procedure, the formation resistivity factor is usually measured only for a relatively few core plugs representing the entire cored interval, which may be several hundred feet. Clearly this leads to large statistical uncertainties due to the small number of samples. In addition, this method does not display the spatial variations of the formation resistivity factor within, or along, the core.
The oil industry is of course also interested in determining the hydraulic permeability of a core sample, which is a measure of its ability to sustain fluid flow under an applied pressure gradient. The permeability is defined from Darcy's law: ##EQU1## where Q is the fluid flow in cm.sup.3 /sec, K is the permeability in Darcy's, A is the cross-sectional area in square cm.sup.2, .DELTA.P/.DELTA.L is the pressure gradient in atmospheres across a length .DELTA.L in cm, and .mu. is the viscosity in centipoise. The permeability K is measured in the laboratory on core plugs by confining the plugs in a sleeve, applying a known pressure gradient, and measuring the flow rate. Again, as in laboratory measurements of formation resistivity factor, the procedure is laborious, time-consuming, expensive, and suffers from small numbers of samples.
These and other limitations and disadvantages of the prior art are overcome by the present invention, however, and an improved method for determining transport characteristics of porous samples with NMR imaging is provided.